Solve for $x$ and $y$ using elimination. $\begin{align*}-5x-7y &= 1 \\ 6x+2y &= 6\end{align*}$
Answer: We can eliminate $x$ when its corresponding coefficients are negative inverses. Recalling our knowledge of least common multiples, multiply the top equation by $6$ and the bottom equation by $5$ $\begin{align*}-30x-42y &= 6\\ 30x+10y &= 30\end{align*}$ Add the top and bottom equations. $-32y = 36$ Divide both sides by $-32$ and reduce as necessary. $y = -\dfrac{9}{8}$ Substitute $-\dfrac{9}{8}$ for $y$ in the top equation. $-5x-7( -\dfrac{9}{8}) = 1$ $-5x+\dfrac{63}{8} = 1$ $-5x = -\dfrac{55}{8}$ $x = \dfrac{11}{8}$ The solution is $\enspace x = \dfrac{11}{8}, \enspace y = -\dfrac{9}{8}$.